Looks really nice. I think having the view perspective skew is annoying and distracting. I think you should get rid of the skew, but that's just me.

Why doesn't it write to Apple Calendar? I only use that and this wouldn't work for me as a result. I'm not much of a calendar person, so probably not for me either way. But to have that read-only removes any possibility that I could use it.

Congrats! Looks nice and the mechanics shown in the previews seem great.